Difficulty: Easy
Correct Answer: Correct
Explanation:
Introduction: De Morgan transformations are core tools for switching between sums with inversion and products with inverted variables. Understanding how NOR relates to AND with inverted inputs lets you re-express logic while preserving functionality.Given Data / Assumptions:
Concept / Approach: De Morgan states: NOT (A + B) = (NOT A) (NOT B) and NOT (A B) = (NOT A) + (NOT B). Therefore, a NOR function is equivalent to an AND of complemented inputs. These two expressions generate identical truth tables because they are algebraically equivalent.Step-by-Step Solution:
Step 1: Start with X = NOT (A + B).Step 2: Apply De Morgan: X = (NOT A) (NOT B).Step 3: Conclude NOR equals AND of inverted inputs; truth tables match exactly.Verification / Alternative check:
Construct truth tables for both forms across all 4 input pairs (00, 01, 10, 11); outputs match in every row.Why Other Options Are Wrong:
Incorrect: Violates standard Boolean identities.Only for two inputs / Only for three or more inputs: De Morgan laws apply for any number of inputs.Common Pitfalls:
Confusing NOR with NAND relationships.Forgetting that distribution of NOT across operators flips OR to AND and vice versa.Final Answer:
Correct
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